theory of fuzzy sets is presented in the section of applied mathematics, which is devoted to methods of uncertainty analysis of data describing the uncertainty of the real events and processes using the concepts of sets no clear boundaries.
Classical set theory defines the membership of a particular element of a particular set.Thus, under the membership accepted concepts in binary terms, iethere is a clear condition that the element in question, or belongs or does not belong.
Set theory regarding the vagueness provides graded understanding supplies the element specific to the set, and the degree of its accessories to be described with the appropriate functions.In other words, the transition from a given set of accessories to some elements not belonging does not occur abruptly, but gradually, using a probabilistic approach.
sufficient experience of foreign and domestic researchers indicates insecurity and inadequacy of the probabilistic approach used as a tool for solving weakly structured type.Using statistical methods for solving this type of problem leads to a significant distortion of the original problem statement.That's shortcomings and limitations associated with the use of classical methods of solving semistructured form, are a consequence of the principle of "incompatibility", which is formulated in the theory of fuzzy sets developed by LAZadeh.
Therefore, some foreign and domestic researchers have developed methods for estimating the risk of investment projects and the efficiency of using the tools of the theory of fuzzy sets.They are to replace the method of distribution of probability distribution of opportunities come, which is described by the membership function of the fuzzy type.
Fundamentals of set theory is based on the tools that are related to the methods of decision-making in an uncertain environment.Their use is expected formalization of baselines and performance target orientation as a vector of fuzzy interval (interval values).Contact with each such interval may be characterized by a degree of uncertainty.
Using arithmetic when working with such fuzzy intervals, experts can be obtained by fuzzy interval for a particular target.Based on the initial information, experience and intuition, experts can provide qualitative and quantitative characteristics of the boundaries (intervals) of possible values of the parameters of the field and their possible values.
Set theory can be actively used in practice and in the theory of systems management in the finance and economy to meet the challenges of uncertainty, provided the basic indicators.For example, such a technique, like cameras and some washing machines, equipped with fuzzy controllers.
In mathematics, set theory proposed by LAZadeh, allows us to describe the fuzzy knowledge and concepts to operate them and make vague conclusions.Due to this theory, based on the methods of construction of fuzzy systems using computer technology greatly expands the application of computers.Recently, management fuzzy sets is one of the productive areas of research.The usefulness of fuzzy control is manifested in a certain complexity of technological processes from the standpoint of analysis using quantitative methods.Also, management fuzzy sets used in the qualitative interpretation of the various sources of information.
